Abstract

This is the second part of a work dealing with a low-order mixed finite element method for a class of nonlinear Stokes models arising in quasi-Newtonian fluids. In the first part we showed that the resulting variational formulation is given by a twofold saddle point operator equation, and that the corresponding Galerkin scheme becomes well posed with piecewise constant functions and Raviart-Thomas spaces of lowest order as the associated finite element subspaces. In this paper we develop a Bank-Weiser type a posteriori error analysis yielding a reliable estimate and propose the corresponding adaptive algorithm to compute the mixed finite element solutions. Several numerical results illustrating the efficiency of the method are also provided. © 2003 Elsevier B.V. All rights reserved.